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New Representations and Properties of the m-Weak Group Inverse

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Abstract

Our main goal is to present new representations and properties of the m-weak group inverse which presents a generalization of the weak group inverse, the generalized group inverse, the group inverse and the Drazin inverse. Consequently, we obtain new properties of the generalized group inverse and recover some properties of the weak group inverse and the Drazin inverse. Our results are illustrated by numerical examples. An equivalent condition for the continuity for the m-weak group inverse is studied too. Applying the m-weak group inverse, solvability of several linear equations and their solutions are considered.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000, Niš, Serbia

    Dijana Mosić

  2. College of Sciences, Northeast Electric Power University, Jilin, People’s Republic of China

    Daochang Zhang

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  1. Dijana Mosić
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  2. Daochang Zhang
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Correspondence to Daochang Zhang.

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D. Mosić is supported by the Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 451-03-47/2023-01/200124 and by the project “Linear operators: invertibility, spectra and operator equations” supported by the Branch of SANU in Niš, Grant No. O-30-22. The corresponding author is supported by the National Natural Science Foundation of China (NSFC) (No. 11901079; No. 61672149), and China Postdoctoral Science Foundation (No. 2021M700751), and the Scientific and Technological Research Program Foundation of Jilin Province (No. JJKH20190690KJ, No. 20200401085GX, No. JJKH20220091KJ).

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Mosić, D., Zhang, D. New Representations and Properties of the m-Weak Group Inverse. Results Math 78, 97 (2023). https://doi.org/10.1007/s00025-023-01878-7

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